Ikatan Ahli Teknik Perminyakan Indonesia

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1 Ikatan Ahli Teknik Perminyakan Indonesia Simposium Nasional dan Kongres X Jakarta, November 2008 Makalah Profesional IATMI Optimization Of Super Light Weight Completion Fluids Using Fractional Factorial Design Munawar Khalil a,b Badrul Mohamed Jan a,b a Department of Chemical Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia b Society of Petroleum Engineers Abstract Underbalanced perforation is widely known as one of the best technique to increase hydrocarbon flow. Numerous researchers have proved that the resulting production increases is due to the surge of hydrocarbon that eliminate permeability damage around the perforation tunnel. In order to achieve the underbalance condition downhole, super light weight fluids needs to be formulated. The formulated fluid has lower density compared to the existing fluid in the market. In this research, optimization formulation of super light weight completion fluids was conducted based on experimental design software. There are 4 optimized factors being optimized namely the amount of homogenizing agent (A), amount of additive (B), mixing speed (C) and mixing time (D). Model equation was proposed with regard to the mentioned factors. The results shows that the optimized condition of the formulation is 4% w/w of homogenizing agent, 10% w/w of additive and mixed at rpm during 1 hour. The desirability of the optimized condition is Introduction In the upstream oil and gas industry, perforation is referred to small holes made at the portion of the production casing which connects to the production zone. This connection provide path for hydrocarbon to flow from the reservoir up to the surface. It has been proven in the literatures that during perforation operation, rock around the perforation tunnel will be squeezed and compacted as the perforation bullets enter the formation (Behrmann et al., 1996; Jilani et al. 2002; Smith et al 1997). This process can result low-permeability crushed zone as the primary cause of wellbore damage. In order to minimize this damage, underbalanced perforating should be considered (Jan et al. 2007; King et al. 1986). Underbalaced perforating is a perforation conducted when wellbore pressure is lower than the reservoir pressure (King et al. 1986). It is generally regarded as one of the best methods of creating open and undamaged perforations. The benefits of underbalanced perforation extend far beyond a producer s ability to utilize previously hardto-harvest oil and gas. In addition, it also helps to minimize damage to under-pressurized hydrocarbon pools or formations prone to lost circulation; increased drilling rates have been observed with certain rock types; bit life may be extended; reduced chip holdown occurs, allowing the bit to continuously cut new rock which is then swept away by the drilling fluid; and, oftentimes, well stimulation can be eliminated, further protecting damage-prone formations (Wong and Arco 2003). It has been reported that an underbalanced perforation condition could be achieved by formulating a stable fluid with IATMI

2 non-damaging chemical properties that would have a significantly lower density which called as completion fluid (Jan et al. 2007; Wong and Arco 2003). Jan et al. in 2003 had successfully formulate a super light weight completion fluid which consist of Shell Sarapar 147 synthetic oil [Shell MDS (M)], 3M TM Glass Bubbles as a density reducing agent and an appropriate rheology control agent. The measured density of the formulated completion fluids is around 5.0 ppg. The measured value is much lower than the existing completion fluids in the market which is around 7.57 ppg. Field test has also shown the increase of production rate after perforation job was conducted with fluids based on the optimized formulation from laboratory (Jan et al. 2007). In order to optimize the formulation, it is necessary to perform critical parameters optimization. Such parameters include the amount of rheology controlling agent, amount of additive, speed of mixing, and mixing time. Fractional factorial experimental design was used to evaluate the significance the variables, as well as their interactions (Morgan 1991). It is well known that the number of experimental runs increase geometrically with the number of model parameters (factors). For example, a model with 8 factors would need 2 8 = 256 experimental runs in order to investigate all the single and interaction between them (Montgomery 1997). From the mathematical and statistical point of view, it is not necessary to conduct complete parameter variation in order to optimize the factors since not all of the parameter interactions have appreciable effects on the model results (Akgüngör & Yildiz 2007). Thus, only the fraction of whole experimental runs in factorial design is performed for the sensitivity analysis. Materials and Methods 2.1 Materials To formulate the super light weight completion fluids, synthetic oil based completion fluids were used. The completion fluids are Shell Sarapar 147 synthetic oil [Shell MDS (M)]. 3M TM Glass Bubbles (HGS) were used as a density reducing agent. Homogenizing agent was used as rheology controlling agent in order to suspend the glass bubbles in homogenous slurry, and additive was used to increase the stability. For the determination of density, a 25 ml picnometer was used. The rheological measurements were conducted by a HAAKE VT 550 shear rate controlled-viscometer (Gebruder Haake GmbH, Karlsruhe, Germany). For the slurry mixing, disperser T25 (IKA LABORTECHNIK, Germany) was used. 2.2 Formulation of super light weight completion fluids To formulate super light weight completion fluids, firstly, 65 % w/w of completion fluids was mixed manually with additive. The amount of additive was optimized from 1 % w/w until 10 % w/w. Secondly, 35 % w/w of glass bubbles was mixed with the homogenizing agent. The amount of homogenizing agent was optimized from 1 % w/w until 4 % w/w. The solution of the completion fluids and additive was placed under homogenizer, and the powder mixture (glass bubbles and homogenizing agent) was added slowly into the solution. The slurry was agitated at various speeds and mixing time. Finally, other variables of response such as density, plastic viscosity, and stability were also determined. 2.3 Experimental Design Since a full factorial design is introduced to the experimental design with k factors, there would be 2 k experimental runs. However, as we discus earlier, it is not necessary to investigate the whole 2 k experimental runs. In a two level half fractional factorial design experimental, each factor was assigned as two levels: low (-1.000) and high (1.000). If k factor are considered, there will be 2 k - 1 measurements in order to perform the analysis. In order to gain the accuracy, at least one replicate must be conducted. Into the bargain, it is necessary to conduct at least one central point measurement in order to test for quadratic term within the low-to-high range (Abdul-wahab & Abdo 2007). Therefore, the total number of test is given as: N = r2 k 1 + C (1) Where N represents the total number of test, r is the number of replicates, and C represents the number of center-point measurements. The aims of this optimization are to get the minimum density of the slurry in order to perform underbalanced perforation condition, to gain the stability of the fluid, and to minimize the viscosity. In this research 4 critical factors of formulating super light weight completion fluids, k = 5, i.e. A (amount of homogenizing IATMI

3 agent), B (amount of additive), C (speed of mixing), and D (time of mixing) were investigated. The coded level for these factors is given in table 1. Since two tests are made for each combination (r = 2) to estimate for the pure error, and three center-point measurement are conducted in the analysis (C = 3) to estimate curvature in the model, it was resulted in a total N = 19 experimental measurements based on equation 1. Table 2 represents the experimental design using fractional factorial design which used in this research, the extra experimental measurements (center-point measurements) were collected at mid-level (coded as zero). Experiments were randomized to maximize the effects of unexplained variability in the observed responses, due to extraneous factors. The statistical software was used in order to model building, experimental design, and data analysis. The effect of each factors and their interactions were considered to three parameters, i.e. density of the slurry, plastic viscosity, and stability. Results and Discussions 3.1 Response Analysis The software was used in the statistical analysis investigation. Using this software, half-normal plot in which the ranks of the absolute value of various effects were measured. Figure 1 shows the half normalnormal plot for density as the response variable. Based on figure 1, the factor that lie along the line are negligible and the rest of the factors and their cross interaction are significant. In figure 1, it can be seen that speed of mixing (C), time of mixing (D), the interaction between the amount of homogenizing agent and amount of additive (AB), and the interaction between amount of homogenizing agent and time of mixing (AD) are significant to the density of slurry. The effects of the factor are calculated by averaging the responses of each factor at the plus levels and subtracting the average at the minus levels for the same factor (Abdul- Wahab & Abdo 2007). Similar analysis for the significant factors and their interaction was also conducted to other responses, i.e. plastic viscosity and stability. Figure 2 and 3 show the half-normal plot for those two responses respectively. Based on figure 2, there are 6 terms as the significant factor for the effects, i.e. speed of mixing (C), the interaction between amount of homogenizing agent and time of mixing (AD), the interaction between amount of homogenizing agent and speed of mixing (AC), time of mixing (D), amount of homogenizing agent (A), and amount of additive (B). Afterwards, based on figure 3 the significant terms are amount of homogenizing agent (A), amount of additive (B), the interaction between amount of homogenizing agent and additive (AB), the interaction between amount of homogenizing agent and speed of mixing (AC), the interaction between amount of homogenizing agent and time of mixing (AD), and speed of mixing (C). Before the conclusion from the analysis of variance was adopted, the adequacy of the underlying model should be checked by examination of residual. The normal probability plot is a graphical technique for assessing whether or not a data set is approximately normally distributed. Figure 4 presents a normal probability plot of the residual for density, plastic viscosity, and stability respectively. Figure 4(a) and 4(b) indicate that the model was adequate and it is also normally distributed for those three responses. However based on figure 4(c), the model for stability does not seem to be normally distributed. It is proved by the data doesn t resemble to the straight line. Hence, it is necessary to check another transformation that could have been applied using Box-Cox plot. 3.2 Box-Cox Transformation Normal plot of residual for stability indicates that the model doesn t seem to be normally distributed. Hence, it is necessary to conduct the Box-Cox transformation check. Figure 5 shows the Box-Cox plot for stability. It is recommended to used square root transformation (Lambda = 0.5) with k = Residual Analysis In order to check on the equality of variance, residual versus predicted plot was investigated. Figure 7 shows the residual versus predicted plot for density. From this figure, it seems that the equality of variance is not violated. The same indication also obtained at the rest of responses (plastic viscosity and stability). 3.4 Regression Analysis Using the software, it is possible to develop the model equation in order to predict IATMI

4 the outcome depending on the level for each factor. This equation called the coded equation since the +1 and -1 values are used to represent high and low levels, respectively. In inverse, if the actual values are used, there would be actual equation. Equation 2, 3, and 4 show the coded equation for density, plastic viscosity, and stability respectively. R 2 value for those model was very high, i.e for density (equation 2), for plastic viscosity (equation 3), and for stability (equation 4). Density = * A * B * C * D * A * B E-003 * A * C * A * D (2) plastic viscosity = * A * B * C * D * A * B * A * C * A * D (3) stability = * A * B * C * D * A * B * A * C * A * D (4) 3.5 Optimal Design In order to get the best condition for formulating super light completion fluids, a fractional factorial experimental design tests were investigated. Figure 8 shows ramps of various as the solution to the optimization job. It was obtained that 4% w/w of homogenizing agent, 10% w/w of additive and mixed at rpm during 1 hour as the best condition with the desirability = The software also provides the optimal design in different desirability factors. Table 3 presents the alternative solution for optimal design at other desirability. Conclusion In order to get underbalanced condition in the borehole during perforation job, low density of the slurry, low viscosity and higher stability should be important. A fractional factorial design was develop for optimizing super light completion fluids. The result have shown that speed of mixing (C), time of mixing (D), the interaction between the amount of homogenizing agent and amount of additive (AB), and the interaction between amount of homogenizing agent and time of mixing (AD) are significant to the density of slurry. Then, for the plastic viscosity, the significant terms are speed of mixing (C), the interaction between amount of homogenizing agent and time of mixing (AD), the interaction between amount of homogenizing agent and speed of mixing (AC), time of mixing (D), amount of homogenizing agent (A), and amount of additive (B). and finally, for stability, the terms are amount of homogenizing agent (A), amount of additive (B), the interaction between amount of homogenizing agent and additive (AB), the interaction between amount of homogenizing agent and speed of mixing (AC), the interaction between amount of homogenizing agent and time of mixing (AD), and speed of mixing (C). The model was tested for its adequacy using normal plot residual and found that the assumption of normality and independency are not violated except for stability. Then, Box-Cox transformation have suggested square root transformation (Lambda = 0.5) with k = 0.2. R 2 value was very high, that suggesting that model accounted for most of the variability. The optimal solution with specified desirability was calculated using the software and presented. The selected solution is 4% w/w of homogenizing agent, 10% w/w of additive and mixed at rpm during 1 hour as the best condition with the desirability = References Abdul-Wahab, S.A., Abdo, J Optimization of multistage flash desalination process by using a two-level factorial design. Applied Thermal Engineering. 27, Akgüngör, A.P., Yildiz, O Sensitivity analysis of an accident prediction model by the fractional factorial method. Accident Analysis and Prevention. 39, Behrmann, L.A., Huber, K., McDonald, B., Couet, B., Dees, J., Folse, R., Handren, P., Schmidt, J., Snider, P., Quo Vadis, Extreme Overbalance?. Oilfield Review 8, no. 3 (Autumn 1996): Jan, B.M., Rae, G., Noor, I., Suhadi, A.N., Devadass, M., Increasing production by maximizing underbalance during perforation. Paper SPE presented at the 2007 International Oil Conference and Exhibition, Veracruz, Mexico, Jilani, S.Z., Menouar H., Al-Majed A.A., Khan M.A., Effect of overbalance pressure on formation damage. J. Pet. Sci. Eng. 36, IATMI

5 King, G.E., Anderson, A.R., Singham, M.D A field study of underbalance pressure necessary to obtain clean perforating using tubing-conveyed perforating. Paper SPE presented at the 1986 SPE Annual Technical Conference and Exhibition, Las Vegas, September. Montgomery, D.C., Design and analysis of experiments fifth edition. John Wiley & Sons, Inc: New York. Morgan, E., Chemometrics: experimental design. John Wiley & Sons, Inc: London. Smith, P.S., Behrmann, L.A. Yang,W., Improvements in perforating performance in high compressive strength rock. Paper SPE 38141, presented at the SPE European Formation Damage Conference, The Hague, The Netherlands, June 2-3. Wong, A, Arco, MJ., Use of hollow glass bubble as a density reducing agent for drilling. Paper No presented at CODE/CAODC drilling conference, Calgary, Alberta Canada, October. Wong, A., Arco, M.J., A new technology for reducing the density of drilling fluids. 3M Specialty Materials Figure 1 Half-normal plot of density. Figure 2 Half-normal plot of plastic viscosity. Figure 3 Half-normal plot of stability. IATMI

6 (a) (b) (c) Figure 4 Normal plot of residual for the responses; (a) for density, (b) for plastic viscosity, (c) for stability. Figure 5 Box-Cox plot for stability. IATMI

7 Figure 6 Normal plot of for stability after Box Cox transformation. Figure 7 Residual versus predicted plot for density. IATMI

8 Desirability = Figure 8 Ramps for various factors. IATMI

9 Table 1 Coded levels for independent factors used in the experimental design Factors Symbols Coded Level Low (-1) High (1) Amount of homogenizing agent (% A 1 4 w/w) Amount of additive (% w/w) B 1 10 Speed of Mixing (rpm) C Time of Mixing (Hours) D 1 3 Table 2 Experimental design used in fractional factorial design studies by using for independent variables and three dependent variables Experi ments Coded Level A B C D Amount Speed of of Mixing Additive (rpm) (% w/w) Amount of Homogenizing agent (% w/w) Time of Mixing (Hours) Density (ppg) Responses Plastic viscosity (cp) Stabilty (Days) 1 0 (2.5) 0 (5.5) 0 (14500) 0 (2) (4) 1 (10) 1 (24000) 1 (3) (2.5) 0 (5.5) 0 (14500) 0 (2) (4) 1 (10) -1 (5000) -1 (1) (1) -1 (1) 1 (24000) 1 (3) (4) -1 (1) 1 (24000) -1 (1) (2.5) 0 (5.5) 0 (14500) 0 (2) (1) -1 (1) -1 (5000) -1 (1) (1) -1 (1) -1 (5000) -1 (1) (4) -1 (1) -1 (5000) 1 (3) (4) 1 (10) 1 (24000) 1 (3) (4) -1 (1) 1 (24000) -1 (1) (4) -1 (1) -1 (5000) 1 (3) (1) 1 (10) -1 (5000) 1 (3) (1) -1 (1) 1 (24000) 1 (3) (4) 1 (10) -1 (5000) -1 (1) (1) 1 (10) 1 (24000) -1 (1) (1) 1 (10) -1 (5000) 1 (3) (1) 1 (10) 1 (24000) -1 (1) IATMI

10 Table 3 Optimal Solution Solution Number Amount of Homogenizing agent Amount of Additive Speed of Mixing Time of Mixing Density Plastic Viscosity Stability Desirability 1* 4.00* 10.00* * 1.00* * * 4.190* * * selected solution IATMI